Geometry (QUADRILATERAL PARALLELOGRAMS THEOREMS PART 2)

Theorem 4-14

If a diagonal is drawn in a parallelogram, then two congruent triangles are formed.

Match the following reasons with the statements given to create the proof.

1. DO = OB, AO = OC 2. <DOC = <AOB 3. Triangle COD congruent to Triangle AOB 4. <1 = <2, AB = DC 5. AB||DC 6. ABCD is a parallelogram 1. Given 2. If two sides = and ||, then a parallelogram. 3. SAS 4. CPCTE 5. If alternate interior angles =, then lines parallel. 6. Vertical angles are equal.

Match the reasons to the statements given.

1. Parallelogram ABCD 2. BT = TD 3. <1 = <2 4. BC||AD 5. <3 = <4 6. Triangle BET congruent to Triangle DFT 7. ET = TF 1. Given 2. 3. CPCTE 4. If lines parallel, then alternate interior angles are =. 5. 6. 7.

Which of the following are quadrilaterals?

A quadrilateral is a geometric figure with four sides. trapezoids rectangles squares parallelograms

parallelogram

A quadrilateral with both pairs of opposite sides parallel.

Which of the following reasons would complete the proof in lines 3 and 5? https://internationalvla.sooschools.com/media/g_geo_ccss_2016/4/page77a.gif

Definition of parallel.

Theorem 4-18

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Theorem 4-16

If two sides of a quadrilateral are equal and parallel, then the quadrilateral is a parallelogram.

Corollary 1

Opposite angles of a parallelogram are equal.

Corollary 2

Opposite sides of a parallelogram are equal.

Theorem 4- 15

The diagonals of a parallelogram bisect each other.

Corollary 3

Two parallel lines are equidistant throughout.

A parallelogram is __________________ a quadrilateral.

always

A quadrilateral is ___________ a parallelogram.

always

If a diagonal is drawn in a parallelogram, then two congruent triangles are ________ formed.

always

Review the image and two-column proof below. https://internationalvla.sooschools.com/media/g_geo_ccss_2016/4/page77c.gif Which of the following represents a valid reason for statement #2?

opposite sides of a parallelogram are equal.

The diagonal of a parallelogram ____________ creates alternate interior angles.

sometimes